Estimation of compositeness with correction terms

TL;DR

This paper improves the estimation of the compositeness in bound states by introducing correction terms and uncertainty bands, enabling more accurate interpretation of the composite structure in physical systems.

Contribution

It presents a quantitative method to estimate correction terms in the weak-binding relation, ensuring the compositeness remains within its probability bounds.

Findings

Estimated compositeness for physical systems as a fraction of the composite component.

Proposed an uncertainty band method to account for correction terms.

Enhanced the interpretability of compositeness in systems with large scattering length.

Abstract

The compositeness $X$ is defined as the probability to observe the composite structure such as the hadronic molecule component in a bound state. One of the model-independent approaches to calculate $X$ is the weak-binding relation. However, when the scattering length $a_{0}$ is larger than the radius of the bound state $R$, the central value of the compositeness $X$ becomes larger than unity, which cannot be interpreted as a probability. For the systems with $a_{0}>R$, we need to estimate the compositeness with the correction terms. For the reasonable determination of the compositeness, we first present the quantitative estimation of the correction terms. Because the exact value of the compositeness should be contained in its definition domain $0\leq X\leq 1$, we propose the reasonable estimation method with the uncertainty band by excluding the region outside of the definition domain of the compositeness. We finally estimate the compositeness of physical systems, and obtain the result which we can interpret as the fraction of the composite component.